Question

Apps 3. G Gmail YouTube Maps -11 POINTS SCALCET8 4.1.029. Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) F(x) = 9 + 1x - * Submit Answer -/1 POINTS SCALCET8 4.1.030. Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) P(X) = x++ 3x2 - 105X - /2 POINTS SCALCET8 4.1.048. Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 3 + 54x - 2x], [0, 4] absolute minimum value absolute maximum value

Answer 1

froid = 9+ 2x - ₂ x ² To find Critical numbers- Find f'c and put it canal to zero. = لم میدم 1 -232 = 0 so i critical number. I'x = 1 (6 fortsut 24 a f(x) = x² + 3x²_1059 f'cu) = 3.202 +624-105 70 302?+22-35) = = 33+73-51-35 30 - * (*+7) -5(+7) (2-5) (x+7) =0 2= 5, 22-7 bo Critical numbers are- 1235,-

f(x) = 3+ 54% -223, (0.4] - let's find critical point f'(x) = 54-622=0 6x²= sy og Bee -3, 31. Now for maxim or minime. Check Sign of f(x) at critial point The Boundray point [ou] the and if if fcxyco f(x) >0 Then Then fox for has local maxima has local mining And we have foxy = 54-622 f' CM) = -12% NOLO at a=-3 f(n) = 36 >o le mining f') = -36 <0 ie maxima at a-3 260 t any co at x = 4 f (n) = -48 Lo making

est a=-3 we have and miming maxima cat at x=3 and x=y Now for abosolute maximum find maximum value of f(n) f(x) = 3+54 n - 223 f(+3) = 3+54*3-2(27) fm = 11! Now f(4) = 3 +5444 - 2864 = 91 so absolute maximum is at a=3 and its value is 1 11 And Absolate minimum is at X=-3 and it's value. is f(-3) - 3 - 541x3 - 24-29) Algolete miminate flos) Absolute minimuna -105